Question: Simplify the following expression: $\sqrt{125}-\sqrt{45}+\sqrt{80}$
Explanation: First, try to factor any perfect squares out of the radicals. $= \sqrt{125}-\sqrt{45}+\sqrt{80}$ $= \sqrt{25 \cdot 5}-\sqrt{9 \cdot 5}+\sqrt{16 \cdot 5}$ Separate the radicals and simplify. $= \sqrt{25} \cdot \sqrt{5}-\sqrt{9} \cdot \sqrt{5}+\sqrt{16} \cdot \sqrt{5}$ $= 5\sqrt{5}-3\sqrt{5}+4\sqrt{5}$ Finally, simplify by combining the terms. $= ( 5 - 3 + 4 )\sqrt{5} = 6\sqrt{5}$